How can I make certain vertices unselectable?
To avoid separating the vertices into a new object you can use Vertex Groups

Select the vertices you want to group.

Make a new vertex group (With the + sign) and assign the selected vertices to it.

To hide those vercices press H

To unhide press H



Once you've created and asigned vertex groups is very easy to select and unselect groups of vertices as you need. Vertex groups can be named, edited or deleted.

Vertex groups are also of particular importance if you are going to be using cloth simulation.

More information on the blender manual:

https://docs.blender.org/manual/en/dev/modeling/meshes/properties/vertex_groups/assigning_vertex_group.html?highlight=vertex%20groups